THE SEARCH FOR DIFFERENTIAL-EQUATIONS FOR CERTAIN SETS OF ORTHOGONAL POLYNOMIALS

[摘要] We look for differential equations of the form SIGMA(i=0)(infinity)c(i)(x)y(i)(x) = 0, where the coefficients {c(i)(x)}i=0infinity are continuous functions on the real line and where {c(i)(x)}i=1infinity are independent of n, for the generalized Jacobi polynomials {P(n)alpha,beta,M,N(x)}n=0infinity and for generalized Laguerre polynomials (L(n)alpha,M,N(x)}n=0infinity which are orthogonal with respect to an inner product of Sobolev type. We use a method involving computer algebra packages like Maple and Mathematica and we will give some preliminary results.

[发布日期] 1993-12-31

[效力级别]  Proceedings Paper

[关键词] DIFFERENTIAL EQUATIONS;SOBOLEV-LAGUERRE POLYNOMIALS;GENERALIZED POLYNOMIALS